# Multiscale Modeling of Polycrystalline NiTi Shape Memory Alloy under Various Plastic Deformation Conditions by Coupling Microstructure Evolution and Macroscopic Mechanical Response

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## Abstract

**:**

## 1. Introduction

## 2. Modeling Methodology

#### 2.1. Macroscale Finite Element Model

_{50.9}Ti

_{49.1}(at.%) by means of electro-discharge machining (EDM). In addition, the as-received NiTi SMA bar was prepared by virtue of vacuum induction melting method and subsequent rolling at 800 °C. In the case of canning compression, the NiTi SMA sample was canned in the low carbon steel cans with the inner diameter of 4 mm and the outer diameter of 10 mm. The elastic and plastic data used in macroscale finite element simulation is directly obtained from the mechanical response of NiTi SMA subjected to uniaxial compression at 400 °C at the constant strain rate of 0.001 s

^{−1}by using an INSTRON-5500R universal testing machine (Instron Corporation, Norwood, MA, USA) equipped with a heating device. In this way, this model provides general distribution of displacement, strain and stress at the macroscale level.

#### 2.2. Microscale Finite Element Model

#### 2.3. Crystal Plasticity Constitutive Model

## 3. Results and Discussion

#### 3.1. Distribution of Stress and Strain at Macroscale

#### 3.2. Distribution of Stress and Strain at Microscale

#### 3.3. Distribution of Dislocation at Microscale

^{15}m

^{−2}in the case of uniaxial compression and the corresponding value in the case of canning compression is 3.15 × 10

^{15}m

^{−2}. This can be served as an evidence that at the same deformation degree, canning compression contributes to relieving the SSD density within the deformed sample than uniaxial compression. As a result, canning compression is favorable of sustaining large plastic deformation.

## 4. Conclusions

- (1)
- At the macroscale, it can be concluded that canning compression contributes to relieving the inhomogeneous plastic strain as the compression of the low carbon steel can results in a three-dimensional compressive loading state of NiTi SMA sample.
- (2)
- The sub-model technique in the finite element code ABAQUS is used to extracted the accurate deformation history of selected regions at the macroscale simulation. Then, this deformation history, which reflects the complex interaction between the polycrystalline aggregation and neighboring grains, can serve as boundary conditions used at the microsacle simulation.
- (3)
- At the microscale, it can be concluded that the mitigation of inhomogeneous plastic deformation in canning compression contributes to various microstructure evolution in selected regions. Moreover, the ease of inhomogeneity in plastic strain contributes to reducing the difference of the stress level in various regions and reducing statistically stored dislocation (SSD) density within the deformed NiTi SMA sample. Therefore, canning compression is favorable of sustaining large plastic deformation.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Schematic diagram of the idea of the multiscale method based on the sub-model technique of finite element code ABAQUS.

**Figure 2.**Schematic diagram of NiTi SMA under: (

**a**,

**b**) uniaxial compression process and canning compression process, where zone I showing the minimum deformation zone, zone II showing the principal deformation zone and zone III showing the intermediate deformation zone; (

**c**) material response as the input data of macroscale finite element simulation based on experimental result of NiTi SMA subjected to uniaxial compression at 400 °C at the constant strain rate of 0.001 s

^{−1}.

**Figure 3.**(

**a**) Cross-sectional scanning electron microscope morphology of as-received NiTi SMA and (

**b**) voronoi tessellation generated using NEPER.

**Figure 4.**Macroscale strain and stress distribution of NiTi SMA at the deformation degree of 12%: (

**a**,

**c**) under uniaxial compression process; (

**b**,

**d**) under canning compression process. (Regions 1, 2, and 3 of interest correspond to three characteristic deformation zones during plastic deformation.)

**Figure 5.**Strain distribution at the microscale level during uniaxial compression and canning compression processes with the locations of the polycrystalline models corresponding to regions 1, 2, and 3 in Figure 4.

**Figure 6.**Stress distribution at the microscale level during uniaxial compression and canning compression processes with the locations of the polycrystalline models corresponding to regions 1, 2, and 3 in Figure 4.

**Figure 7.**Contour plots of SSD density at the microscale level with the locations of the polycrystalline models corresponding to region 1 in Figure 4 during: (

**a**) uniaxial compression process and (

**b**) canning compression process; (

**c**) Statistical analysis of SSD density in (

**a**,

**b**).

${\mathit{C}}_{11}$ | ${\mathit{C}}_{12}$ | ${\mathit{C}}_{44}$ | ${\mathit{h}}_{0}$ | ${\mathit{\tau}}_{\mathrm{s}}$ | ${\mathit{\tau}}_{0}$ | ${\dot{\mathit{\gamma}}}_{0}$ | q | n |
---|---|---|---|---|---|---|---|---|

130 GPa | 98 GPa | 34 GPa | 1200 MPa | 322 MPa | 160 MPa | 0.001 s^{−1} | 1.4 | 20 |

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**MDPI and ACS Style**

Hu, L.; Jiang, S.; Zhou, T.; Tu, J.; Shi, L.; Chen, Q.; Yang, M.
Multiscale Modeling of Polycrystalline NiTi Shape Memory Alloy under Various Plastic Deformation Conditions by Coupling Microstructure Evolution and Macroscopic Mechanical Response. *Materials* **2017**, *10*, 1172.
https://doi.org/10.3390/ma10101172

**AMA Style**

Hu L, Jiang S, Zhou T, Tu J, Shi L, Chen Q, Yang M.
Multiscale Modeling of Polycrystalline NiTi Shape Memory Alloy under Various Plastic Deformation Conditions by Coupling Microstructure Evolution and Macroscopic Mechanical Response. *Materials*. 2017; 10(10):1172.
https://doi.org/10.3390/ma10101172

**Chicago/Turabian Style**

Hu, Li, Shuyong Jiang, Tao Zhou, Jian Tu, Laixin Shi, Qiang Chen, and Mingbo Yang.
2017. "Multiscale Modeling of Polycrystalline NiTi Shape Memory Alloy under Various Plastic Deformation Conditions by Coupling Microstructure Evolution and Macroscopic Mechanical Response" *Materials* 10, no. 10: 1172.
https://doi.org/10.3390/ma10101172